65x=13x^2

Solution for 65x=13x^2 equation:

65x=13x^2

We move all terms to the left:

65x-(13x^2)=0

determiningTheFunctionDomain
-13x^2+65x=0

a = -13; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·(-13)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*-13}=\frac{-130}{-26}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*-13}=\frac{0}{-26}
=0
$